I don't understand this fit of anger of the creator of the category, when he canceled my change without reasonable justification. The category name has no meaning for most people: "Pythagorean tiling", so the current link worded "Pythagorean tiling" on the page "Category:Pythagorean theorem" is an obstacle in searches of visual proofs of the Pythagorean theorem.
— Baelde (talk) 12:27, 15 November 2012 (UTC)

I don't understand your hostility towards the topic of Pythagorean tiling. All of your edits seem to be aimed at minimizing this subject in favor of one particular and very specific use of it, as a tool for a proof of the Pythagorean theorem. I don't find this constructive or useful, and I don't like the way your harmful edits have spread from the articles on English Wikipedia to here. —David Eppstein (talk) 16:32, 15 November 2012 (UTC)

I know, you have given to "Pythagorean tiling" the same meaning on Wikipedia and here.

To you a "Pythagorean tiling" is a tiling by squares of two different sizes. So you have created
in "Category:Pythagorean theorem" a subcategory which excludes isosceles triangles, while the theorem
for isosceles right triangles is valid and can be proved through a tiling. Is that reasonable?
— Baelde (talk) 18:51, 15 November 2012 (UTC)

Given your past history of twisting my responses to fit your point of view and then using your misinterpretations as justification for your bad edits, I don't see the point in responding to your questions any more. You do not seem to be looking for understanding, but rather for some misstep that you can use to push your point of view. —David Eppstein (talk) 18:59, 15 November 2012 (UTC)

Instead of considering my arguments,
you are talking about some misstep, so nobody can understand.

As I have already told you, this meaning of "Pythagorean tiling" is given in reference [1] of the Wikipedia Pythagorean tiling article. As for why this category: one of the parent categories, Category:Tessellations, is overcrowded with many images of unrelated tesselations, which can be easier to browse if they are organized into subcategories. This subcategory organization also has the advantage that each subcategory can be put into additional parent categories that are relevant for the subcategory but not for all tesselations; for instance, the Pythagorean tilings are relevant to categories Pythagorean theorem and Wallpaper group p4, and having those as parent categories of this one means that we don't have to (and shouldn't) add the same categories individually to each file in the Pythagorean tiling category. This is the third subcategory of tesselations that I've created or added files to in this way; the first two are Category:Kagome structures and Category:Rhombille tiling. All of these have multiple alternative names; we could have used "two square tiling" for this one, "trihexagonal tiling" for the Kagome one, or "tumbling blocks" for the rhombille one, but we have to pick a single name. —David Eppstein (talk) 20:41, 15 November 2012 (UTC)

We cannot study together these documents supposedly source of the category name.

Often someone searching visual proofs of the Pythagorean theorem
has never read neither heard "Pythagorean tiling", so the current link
worded "Pythagorean tiling" on the page "Category:Pythagorean theorem"
is an obstacle in these searches.

It is not logic to create a subcategory of "Category:Pythagorean theorem"
for right triangles which are not isosceles.

Today I will explain again,
and repeat what you have read previously on Wikipedia and here.
Your subcategory of "Category:Pythagorean theorem" is not reasonable
because your subcategory excludes isosceles triangles, while the theorem
for isosceles right triangles is valid and can be proved through a tiling.
and because its title is unknown for most people. Here is a third objection
very comprehensible: we have to store images by subjects,
and you don't do that with your subcategory.

1. Often someone searching visual proofs of the Pythagorean theorem
has never read neither heard "Pythagorean tiling", so the current link
worded "Pythagorean tiling" on the page "Category:Pythagorean theorem"
is an obstacle in these searches.

To know that, it is sufficient to compare numbers of visitors on two pages of Wikipedia:

2. It is not logic to create a subcategory of "Category:Pythagorean theorem"
for right triangles which are not isosceles.

To know that, it is sufficient to study two assemblages
of five puzzle pieces, that you know because you are the author
of the first image below. A square puzzle piece or one tile is surrounded
by four fractions of the other tile, whatever the initial right triangle,
isosceles or not.

In case of isosceles triangle, all square tiles are not of two different sizes,
and the midpoint of any segment in dashed red, on the second image,
is a common vertex of four congruent tiles.

3. In your subcategory of "Category:Pythagorean theorem", you have stored numerous images
which have to be elsewhere, like the following images.

No trace
of the Pythagorean theorem,
but the image is stored
in your subcategory of
"Cat:Pythagorean theorem" ! ⸮ ⸮

No trace
of the Pythagorean theorem,
but the image is stored
in your subcategory of
"Cat:Pythagorean theorem" ! ⸮ ⸮

No trace
of the Pythagorean theorem,
but the image is stored
in your subcategory of
"Cat:Pythagorean theorem" ! ⸮ ⸮

No trace
of the Pythagorean theorem,
but the image is stored
in your subcategory of
"Cat:Pythagorean theorem" ! ⸮ ⸮

No trace
of the Pythagorean theorem,
but the image is stored
in your subcategory of
"Cat:Pythagorean theorem" ! ⸮ ⸮

No trace
of the Pythagorean theorem,
but the image is stored
in your subcategory of
"Cat:Pythagorean theorem" ! ⸮ ⸮

Through the title "Pythagorean tiling" and the meaning given to it, you have created a problem on Wikipedia and here.
The objection 3 shows your negligence when you created this subcategory of "Category:Pythagorean theorem",
named "Pythagorean tiling": obviously we have to sort images by subjects.
— Baelde (talk) 17:07, 16 November 2012 (UTC)

Frankly, you are coming across as a crank. Your obsessive focus on the Pythagorean theorem, and the fact that this category has a similar title, is causing you to lose sight of the geometry. Ignore the name; consider what's in the category: tilings with two different sizes of squares. It's obviously a well defined geometric category and it's obviously relevant enough to the Pythagorean theorem to be a subcategory. Unless you suddenly start being a lot more rational I don't see the point of further response to your crankery. Expect me to continue reverting your changes without any more comments or explanations. Goodbye. —David Eppstein (talk) 17:17, 16 November 2012 (UTC)

Later, "Category:Wallpaper_group_p4" could be a subject on this page, I don't know.
Today I will talk about a category more or less connected to the Pythagorean theorem. In introduction
of your "Category:Pythagorean_tiling", you wrote that a tessellation of the plane by squares of two different sizes
is a possible base to prove the Pythagorean theorem (see above my objection).
Today your "Category:Pythagorean_tiling" contains 31 images, one only
of them deals with the Pythagorean theorem. You are the author of this only image.
It happened that I had been under your pression when I refused to categorize a few images in your
"Category:Pythagorean tiling": see this discussion, where you have gone away without goodbye. Later, you could
categorize an image in your "Category:Pythagorean_tiling" without assent of authors. The current situation is unstable.
Would you clarify your intention?
— Baelde (talk) 08:08, 17 November 2012 (UTC)